Question

Sin 2x=-1 решение. .

Answer 1

Sin2x = - 1 
2x = - pi/2 + 2pik   // : 2 
x = - pi/4 + pik, k ∈ Z

Answer 2

$\sin2x=-1 \\ 2x=- \frac{\pi}{2} +2 \pi k,k \in Z \\ x=- \frac{\pi}{4} + \pi k,k \in Z$

Answer 3

To solve the equation sin(2x) = -1, we need to find the values of x that satisfy the equation.

The first step is to isolate the sine term by dividing both sides of the equation by -1:

sin(2x) = -1 becomes -sin(2x) = 1

Next, we need to find the angles whose sine value is 1. The angle whose sine is 1 is π/2 or 90 degrees. However, we need to find the angles for which sin(2x) is equal to 1.

Using the double-angle identity for sine, we know that sin(2x) = 2sin(x)cos(x). So we set up the equation:

2sin(x)cos(x) = 1

Now we have two possibilities: either sin(x) = 1 and cos(x) = 1/2 or sin(x) = -1 and cos(x) = -1/2.

For sin(x) = 1 and cos(x) = 1/2:

Since sin(x) = 1, the angle x is π/2 or 90 degrees.

Substituting sin(x) = 1 and cos(x) = 1/2 into the equation 2sin(x)cos(x) = 1, we have:

2(1)(1/2) = 1 1 = 1

This equation is satisfied, so x = π/2 or x = 90 degrees is a solution.

For sin(x) = -1 and cos(x) = -1/2:

To find the angles where sin(x) = -1, we look for the angle x whose sine is -1. The angle whose sine is -1 is -π/2 or -90 degrees.

Substituting sin(x) = -1 and cos(x) = -1/2 into the equation 2sin(x)cos(x) = 1, we have:

2(-1)(-1/2) = 1 1 = 1

This equation is satisfied, so x = -π/2 or x = -90 degrees is also a solution.

Therefore, the solutions to the equation sin(2x) = -1 are:

x = π/2 + 2πn, where n is an integer (for x = 90 degrees + 360 degrees * n)

x = -π/2 + 2πn, where n is an integer (for x = -90 degrees + 360 degrees * n)

These solutions represent all the possible values of x that satisfy the equation sin(2x) = -1.